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AVERAGE AND AGES SUMMARY, Cheat Sheet of Mathematics
AVERAGE AND AGES SUMMARY NOTES QUESTIONS
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Chapter
Average and Ages
Average
Average: Average is defined as the sum of different data (terms) divided by total number of terms
Average =
Totalnumberof terms(N)
Sumof giventerms(S)
Example: Find the average of given terms 2, 3, 4, 5, 6
Sol. Total number of terms = 5
Average =
5
2 3 4 5 6
Some Basic Formulae
- Average of ‘n’ natural number =
(𝑛+ 1 )
2
- Average of ‘n’ even numbers = (n + 1)
- Average of ‘n’ odd numbers = n
- Average of ‘n’ consecutive natural numbers =
Firstnumber+Lastnumber
2
- Average of sum of squares of first ‘n’ natural numbers =
(n+ 1 )(2n+ 1 )
6
Some Important Points:
- If the value of each number is increased by the same value ‘a’, then the average of all numbers will also increase
by ‘a’.
- If the value of each number is decreased by the same value ‘a’, then the average of all numbers will also decrease
by ‘a’.
- If the value of each number is multiplied by the same value ‘a’, then the average of all numbers will also get
multiplied by ‘a’.
- If the value of each numbers is divided by the same value ‘a’, then the average of all numbers will also get divided
by ‘a’.
Some useful Formulae
- If the average of ‘x’ numbers is a and that of ‘y’ numbers is b, then the average of (x + y) numbers =
x y
xa yb
Example: The average of 10 numbers is 15 and that of 15 numbers is 20. Find the average of all 25 numbers?
Sol. Average =
10 × 15 + 15 × 20
10 + 15
150 + 300
25
450
25
- If the average of ‘n’ quantities is equal to ‘x’ when a quantity is removed the average becomes ‘y’. Then the value
of the removed quantity is = [n (x – y) + y]
Example: The average age of 24 men and 1 woman is equal to 35 years. If 1 woman left, the average becomes 34
years. Find the age of woman who left the class?
Sol: Age of women = [25(35 – 34) + 34] = 59 years
- If the average of marks obtained by ‘n’ students in an exam is ‘M’. If the average marks of passed students in ’P’
and that of failed students is ‘F’. Then the number of students who failed in exam is
−
−
P F
n(P M)
No. of failed students =
−
−
Passedaverage Failedaverage
Totalstudents(Passedaverage Totalaverage)
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1. A bastman scores 34, 36, 38, 40, 42, in his five innings
respectively. Find the average runs in the five innings?
Sol. Average runs =
+ + + +
5
4 36 38 40 42
5
190
2. The average of 10 quantities is 12. The average of 6 of
them is 8. What is the average of remaining four
numbers.
Sol. The required average = =
10– 6
10 12 – 6 8
3. Average of marks obtained by 120 candidates in a
certain examination is 35. If the average marks of
passed candidates is 39 and that of the failed
candidates is 15, what is number of candidates who
passed the examination?
Sol. Let the number of passed candidates be x.
Then, total marks = 120 × 35 = 39x + (120 – x) × 15
or, 4200 = 39x + 1800 – 15x
or, 24x = 2400
∴ x =
∴ number of passed candidates = 100.
4. The average salary of the entire staff in a office is Rs.
120 per month. The average salary of officers is Rs.
460 and that of non-officers is Rs 110. If the number of
officers is 15, then find the number of non-officers in
the office.
Sol. Let the required number of non-officers = x
Then, 110x + 460 × 15 = 120 (15 + x)
or, 120x – 110x = 460 × 15 – 120 × 15 = 1 (460 – 120)
or, 10x = 15 × 340; x = 15 × 34 = 510
No. of non-officers = No. of officers ×
−
Mean average – Av. Salary of non officers
Av. salary of officers – Mean average
120 – 110
15 510.
460 – 120
5. The average of the first and the second of three
numbers is 10 more than the average of the second
and the third of these numbers. What is the difference
between the first and third of these three numbers?
Sol. Average of the first and the second numbers
2
First + Second
Average of the second and the third numbers
2
Second + Third
According to the question,
2 2
- = 10
First + second Second + Third
∴ First – Third = 20
6. The average height of 50 students of a class is 152 cm.
If 10 among them whose average height is 148 cm left
the class and 10 new boys of average height 150 cm
are included in the class, then what will be the new
average height of the students of the class?
Sol. The total height of 50 students = 152 × 50 = 7600cm
Total decrease in the height when 10 students left the
class
= 148 × 10 = 1480 cm
Total increase in the height after 10 new students
came
= 10 × 150 = 1500 cm
Now, Total height of 50 students = 7600 – 1480 + 1500
= 7620cm
New average =
50
152.4 cm
7620
7. The sum of the present ages of Hari and Mohan is
x years and y years then
x + y = 2(x – y), x = 3y ... (i)
From the question, (x – 4 + y – 4) =
2
{(x – 4)– (y – 4)}
3
or, 2x + 2y – 16 = 3x – 3y
or, 5y – x = 16 ... (ii)
Solving eqn (i) and (ii),
x = 24 and y = 8
Hari’s age after 12 years = 24 + 12 = 36 years
Mohan’s age after 12 years = 8 + 12 = 20 years
The ratio of their ages = 36 : 20 = 9 : 5
8. The present age of Geeta is 5 year more than the
present age of his brother Mahesh. The present age of
their father is twice the sum of their ages. At the time
of Mahesh’s birth their father’s age was 8 times of the
age of Geeta. Find their present ages.
Sol. Let the present age of Mahesh is x years then the
present age of Geeta will be x + 5 and the present age
of their father will be 2(x + x + 5) = 4x + 10 years.
The age of Geeta at the time of Mahesh’s birth will be
x + 5 – x = 5 years while the age of the father will be 4x
- 10 – x = 3x + 10 years
From the question,
3x + 10 = 5 × 8
or, 3x = 40 – 10 = 30 or, x = 10 years
and x + 5 = 15 and 4x + 10 = 50 years
So, the ages of Mahesh, Geeta and their father are 10,
15 and 50 years respectively.
Solved Example
double the difference of their present ages. Four years
ago this ratio was one and half times. Find the ratio of
their ages after 12 years.
Sol. Let the present ages of Hari and Mohan be respectively
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1. The mean of 19 observations is 4. If one more
observation of 24 is added to the data, the new mean
will be:
(a) 4 (b) 5 (c) 6
(d) 7 (e) None of these
2. A student bought 4 books for Rs. 120 from one book
shop and 6 books for Rs. 150 from another. The
average price (in rupees), he paid per book was :
(a) 27 (b) 27.50 (c) 135
(d) 138 (e) None of these
3. The average weight of a group of 20 boys was
calculated to be 89.4 kg and it was later discovered
that one weight was misread as 78 kg instead of the
correct one of 87 kg. The correct average weight is :
(a) 88.95 kg (b) 89.25 kg (c) 89.55 kg
(d) 89.85 kg (e) None of these
4. A class has 20 boys and 30 girls. The average age of
boys is 11 years and that of girls is 12 years. What is
the average age of the whole class
(a) 11.6 years (b) 12 years (c) 10 years
(d) 11.2 years (e) None of these
5. What will be the average of even numbers between 11
to 63?
(a) 37.5 (b) 47 (c) 42
(d) 37 (e) None of these
6. The average age of 30 girls is 13 yr. The average of first
18 girls is 15 yr. Find out the average age of remaining
12 girls?
(a) 12 yr (b) 10 yr (c) 16 yr
(d) 10.5 yr (e) None of these
7. The average of nine numbers is 50. The average of the
first five numbers is 54 and that of the last three
numbers is 52. Then, the sixth number is?
(a) 34 (b) 24 (c) 44
(d) 30 (e) None of these
8. A cricketer scored some runs in his continuous 9
innings. He scored 100 runs in his 10th innings and
this increased his average by 8 runs. What was the
average of his runs at the end of 10th innings?
(a) 20 (b) 24 (c) 28
(d) 32 (e) None of the above
9. 10 kg of rice priced at Rs. 12 per kg is mixed with 6 kg
of rice priced at Rs. 16 per kg. Find the average price
of the whole mixture?
(a) Rs. 14 per kg (b) Rs. 14.50 per kg
(c) Rs. 13 per kg (d) Rs. 13.50 per kg
(e) None of these
10. The average temperature from Monday to Thursday is
48°C and from Tuesday to Friday, the average
temperature is 52°C. If the temperature on Monday is
42°C, what was it on Friday?
(a) 46°C (b) 58°C (c) 50°C
(d) 45°C (e) None of these
11. The average of 6 numbers is 8. What is the 7th number
so that average becomes 10?
(a) 22 (b) 18 (c) 21
(d) 20 (e) None of these
12. The average expenditure of a man for the first five
months is Rs. 120 and for the next seven months is Rs.
- His monthly average income if he saves Rs. 290 in
that year, is
(a) Rs. 160 (b) Rs. 170 (c) Rs. 150
(d) Rs. 140 (e) None of these
13. The average salary of 20 workers in an office is Rs.
1900 per month. If the manager’s salary is added, the
average becomes Rs. 2000 per month. The manager’s
annual salary (in Rs) is:
(a) Rs. 24000 (b) Rs. 25200 (c) Rs. 45600
(d) Rs. 48000 (e) None of these
14. A club has 15 men and 25 women. The average age of
men is 10 years and the average age of women is 12
year. What is the average age of the whole club?
(a) 11.40 years (b) 11.60 years (c) 11.25 years
(d) 12.25 years (e) None of these
15. The average of 12 results is 15, and the average of the
first two is 14. What is the average of the rest?
(a) 15.2 (b) 13.2 (c) 15
(d) 16 (e) None of these
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15. S
1
is the series of five consecutive numbers and
average of first three terms is 9. T 1
is series of four
consecutive even number and second lowest term of T 1
is six more than largest term of S 1
. Find the average of
T
1
series?
(a) 19 (b) 17 (c) 15
(d) 21 (e) 23
16. Average of present age of P & R is 33 years. Q is 18
years older than R and Q is 6 years younger than S. If
present age of P is 33
1
3
% less than present age of S,
then find average of present age of Q, R & S.
(a) 44 years (b) 42 years (c) 45 years
(d) 41 years (e) 43 years
17. B’s age is 6 years more than A. If the ratio of B’s age 9
years hence to C’s present age is 9 : 8 & the present age
of C is twice of A’s present age then what will be the age
of B after 5 years.
(a) 18 years (b) 2 5 years (c) 23 years
(d) 24 years (e) 48 years
18. Ratio between age of priya and Swati is 3 : 4. If shikha
is 6 year younger than swati and average age of all
three is 31 years, then find Shikha’s age?
(a) 36 yrs (b) 32 yrs (c) 20 yrs
(d) 24 yrs (e) 30 yrs
19. Four year ago average age of P, Q and R is 33 years. At
present, age of R is three year less than Q and P is three
year older than Q. then find the age of P one year
hence?
(a) 36 years (b) 38 years (c) 40 years
(d) 41 years (e) 36 years
20. Ratio of age of A and B, 6 years ago was 3: 4. Sum of the
present age of B and C is 80 years. C is 12 years elder
to A. Find the difference of B and C’s age five years
later?
(a) 3 years (b) 7 years (c) 6 years
(d) 5 years (e) 4 years
21. Ratio of present age of A and B is 3:2 and four years
later age of B will be 56
1
4
% of age of C. If the average of
the present age of A and C is 54 year then find the
present age of B.
(a) 29 year (b) 27 year (c) 25 year
(d) 32 years (e) 36 year
22. Average of present age of A, B and C is 31 years and C
is one year older than A. If ratio between present age
of B and C is 19 : 14 then find age of B?
(a) 35 years (b) 38 years (c) 34 years
(d) 32 years (e) 42 years
23. Sum of age of Ayush & Anurag is 24 years more than
sum of age of Anurag, Veer & Shivam. Average age of
Veer & Shivam is 59 years. Find average age of Ayush
& Shivam, if Shivam is 24 years older than Veer.
(a) 106.5 years (b) 102.5 years (c) 108.5 years
(d) 110.5 years (e) 116.5 years
24. Rahul’s present age is
4
7
th
of his father’s present age and
four times his sons age three years ago. If the average
of the present age of all three is 33 years then, what is
the difference between the Rahul’s son’s present age
and Rahul’s father’s present age?
(a) 43 (b) 45 (c) 40
(d) 32 (e) 41
25. 5 years ago, age of A is 3 times of the age of B at that
time. Ratio of age of B, 5 year hence, and age of C, 5
year ago, is 3 : 5. If difference between age of C and A
is 10 years(C is younger than A), then find the age of
B.
(a) 20 years (b) 15 years (c) 18 years
(d) 10 years (e) 25 years
26. Suman is 25 yrs elder to his son. If 7 yrs hence, the ratio
of ages of suman and his son will be 2:1, then how
many years back from present suman’s son was born?
(a) 20 yrs (b) 24 yrs (c) 15 yrs
(d) 18 yrs (e) None of these
27. Average of 8 consecutive odd numbers is 10. What will
be the average of smallest 4 numbers out of 8
numbers?
(a) 7 (b) 8 (c) 6
(d) 4 (e) 5
28. Mahesh has two sons named Karan and Arjun. The
ratio of present age of Mahesh and Karan is 5 : 2 and
that of Karan and Arjun is 4 : 3. Also, Karan is 5 years
elder than Arjun. Find the ratio of their ages 10 years
ago.
(a) 10 ∶ 4 ∶ 3 (b) 7 ∶ 2 ∶ 1 (c) 8 ∶ 2 ∶ 1
(d) 8 ∶ 3 ∶ 1 (e) 12 ∶ 6 ∶ 5
29. A person is 16 yrs older than his son. After 2 yrs, the
person’s age will be double the age of his son. Then find
the age of his son 8 yrs hence?
(a) 24 yrs (b) 20 yrs (c) 22 yrs
(d) 18 yrs (e) 28 yrs
30. At present, Suresh is six times his son’s age. 13 years
from now, the ratio of ages of Suresh and his son will
be 11:4 respectively. Find Suresh’s present age?
(a) 36 yrs (b) 48 yrs (c) 30 yrs
(d) 42 yrs (e) None of these
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31. In a 10 overs match, a team has scored runs at rate 7.
in first 6 overs and 8.5 in next 2 over and scored 42
runs in last 2 over. Find overall run rate of the team in
the match.
(a) 10. 40 (b) 10.89 (c) 10.
(d) 10. 43 (e) 10. 23
32. The present age of a son is one- third of that of his
father and 4 yrs hence, the ratio of ages of the father
and the son is 5:2, then find the father’s age 3 yrs ago?
(a) 36 yrs (b) 33 yrs (c) 39 yrs
(d) 30 yrs (e) 27 yrs
33. The average expenditure of Nandu & Bandu on rent is
Rs. 2000 while that on travel is Rs. 1500. Nandu spends
Rs. 800 on food while Bandu spends Rs. 900. What is
average of total expenditure of both? (no one spends
on any other thing than given)
(a) 4400 (b) 4350 (c) 4300
(d) 4750 (e) 4800
34. The sum of Ravi’s and Shivam’s age 4 years ago was 80
years. Ravi’s age 14 years ago was equal to Shivam’s
age 4 years ago, then find the present age of Ravi? (in
years)
(a) 39 (b) 49 (c) 40
(d) 47 (e) 55
35. The average age of 25 men are 60 yrs. If another 5 men
are added whose average age is 30 yrs, then find the
average age of total men?
(a) 50 yrs (b) 55 yrs (c) 60 yrs
(d) 45 yrs (e) 52 yrs
1. Present age of C is 9 less than the sum of present age of
A & B and 6 years hence, age of B will be twice of age of
A. If C is 15 years older than B, then find present age of
D (present age of D is 4 less than the average of present
age of A, B & C).
(a) 41 years (b) 45 years (c) 52 years
(d) 59 years (e) 61 years
2. Average age of Sohan, Mohini and their twin’s daughter
is 22.5 years and average age of Mohini, and her twin’s
daughter is
52
3
years. If average age of Sohan and
Mohini is 37 years, then find average age of Sohan and
his twin’s daughter?
(a) 24 years (b) 16 years (c) 19 years
(d) 18 years (e) 21 years
3. Average marks of class XI are ‘X’ and when average
marks of 15 students reduced by 6, then average marks
of class reduced by 1.875. If number of students in
class XII is 16 more than that of in class XI and total
marks of class XII is 5120, then find average marks of
class XII?
(a) 60 (b) 90 (c) 96
(d) 80 (e) 84
4. Average weight of a family of X members is 18 kg.
When three men of this family get married, average
weight increases by 1kg and when an old man having
weight 18kg more than total weight of wife of these
three men died, average weight become 16 𝑘𝑔. Find
the value of X?
(a) 24 (b) 28 (c) 26
(d) 22 (e) 25
5. Average of four numbers is 64. If 3 is added to first
number, multiplied to second, subtracted from the
third and divided to last one then all the values are
same. Find the difference between 2
nd
highest and the
smallest number?
(a) 45 (b) 35 (c) 42
(d) 39 (e) 32
6. Ratio of present age of Rahul to present age of Gopal is
7 : 8 and ratio of Puneet age four years ago to Rahul age
four years hence is 2 : 3. If present age of Punnet is
75% of present age of Gopal, then find the average of
present ages of Rahul, Gopal and Puneet (in years)?
(a) 37 (b) 40 (c) 35
(d) 42 (e) 44
7. Gurdeep chhabra joined ‘Adda 247’ with the work
experience of 26 years due to which average work
experience of all employees of ‘Adda 247’ was
increased by one year. If initial average work
experience of all employees of ‘Adda 247’ was five
years, then find the new number of employees in ‘Adda
(a) 23 (b) 19 (c) 25
(d) 21 (e) 27
8. Amit’s present age is 75% of Binny’s present age
where as present age of Chintu is
5
8
𝑡ℎ of Binny’s
present age. If difference between difference of Chintu
and Binny age and difference of Binny and Amit age is
6 years then find the average of their age two years
later?
(a) 44 years (b) 42 years (c) 36 years
(d) 40 years (e) 38 years
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Mains Questions
Directions (1-2): Answer these questions based on the
information given below.
There are five members A, B, C, D and E in a family. Ratio of
ages of A and B five years ago was 3: 4. Sum of ages of D and
E five years hence will be 90. If C were born four years later
than his actual date of birth, present Age of
C would be half to that of present age E.
1. What is the age of D four years ago, if the current age
of C is 27 years?
(a) 36 years (b) 34 years
(c) 38 years (d) 30 years
(e) Cannot be determined
2. After 3 years, A will be 20 years old. What is the
average of current ages of A, B, D and E together?
(a) 29 years (b) 29.5 years
(c) 30 years (d) 30.5 years
(e) Cannot be determined
3. 2n years ago, the age of Raju was four times that of his
son and n years ago, the age of Raju was thrice that of
his son. If n years later, the sum of the ages of Raju and
his son will be 80 years, then the difference in the ages
of Raju and his son is
(a) 20 years (b) 40 years
(c) 24 years (d) 30 years
(e) 34 years
4. The sum of the ages of father and son is 50 years. Eight
years ago, the product of their ages was two time the
father’s age at that time, then the present ages (in
years) of the father and son respectively are
(a) 39,6 (b) 35,
(c) 36,9 (d) 40,
(e) None of these
5. Sweta and Neha profess to tell their present ages as 25
and 20 years respectively. (Not original age). Ratio of
their original ages 5 year ago is 5: 4. Sum of ages of both
5 years hence is
400
9
% more than the sum of present
ages of both professed by them. Find the sum of their
present original age
(a) 25 (b) 35 (c) 55
(d) 40 (e) 50
6. Ratio of present age of P and Q is 3: 4. Sum of the
present age of S and P is 41. R is 5 years younger than
Q. Average of present age of Q, R and S is 22 years. Find
the difference of S and R’s age
(a) 3 (b) 2 (c) 1
(d) 5 (e) 4
7. Satish’s age is 4 times the present age of his son’s age.
After 4 year the age of satish become 3 time the age of
his son’s age. If Satish’s wife age is 7/8 of his age then
find out the average of present age of Satish’s wife and
his son.
(a) 18 (b) 20 (c) 14
(d) 16 (e) 21
8. In a company there are 252 employees, in which the
ratio of the number of men and women is 2 : 1. Some
more women are employed and the ratio of men and
women becomes 1 : 1. The average age of all the
employees is now 22 years and the average age of the
women is 2 years less than the average age of the men.
Find the average age (in years) of men and women.
(a) 22,20 (b) 23,
(c) 24,22 (d) 21,
(e) none of these
9. In an exam of Chemistry, three students (X, Y and Z)
participated and got an average score 80. In another
exam i.e. Maths , two students (X and Y) got 20% more
marks then in Chemistry exam while Z got 10% less
marks relative to Chemistry exam. Average mark in
Maths exam is six more than average marks in
Chemistry exam. If difference between score of X and Y
in Maths exam is 24 then find the average of all the
three students in Biology exam if X and Y got 25% more
marks in Biology than Maths exam while Z got only
10% more marks than Maths exam?
(a) 101 (b) 103 (c) 104
(d) 105 (e) 108
10. The average age (in years) of a group of people is twice
the number of people in the group. A person, X, leaves
the group and the average age is still twice the number
of people in the group. Now another person, Y, leaves
the group and the average age is still twice the number
of people in the group. If the ratio of the ages of X and
Y is 19: 17, then find the average age of the group, if
one more person, Z, of age 16 years, leaves the group.
(a) 10 (b) 15 (c) 16
(d) 18 (e) None of these
11. The average age of a husband and wife, who were
married 7 years ago, was 25 years at the time of their
marriage, Now, the average age of the family, including
husband, wife and a child, born during the interval, is
22 years. What is the present age of the child?
(a) 4 yrs. (b) 2 yrs. (c) 3 yrs.
(d) 5 yrs. (e) None of these
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12. The average age of mother, father and son was 42 yrs.
at the time of the marriage of the son. After one year
an infant was born in the family and after 6 yrs of
marriage the average age of the family is 36 years.
What was the age of the bride at the time of marriage.
(a) 25 yrs. (b) 23 yrs. (c) 22 yrs.
(d) 24 yrs. (e) None of these
13. 10 years ago the average age of all the 25 teachers of
the Girls college was 45 years. 4 years ago, the
principal has retired from her post at the age of 60
year. So after one year a new principal whose age was
54 years recruited from outside. The present average
age of all the teachers is, if principal is also considered
as a teacher:
(a) 54
18
25
years (b) 55
17
25
years (c) 49
1
2
years
(d) 49
2
3
years (e) None of these
14. The average price of 80 computers in an electronic
shop is Rs. 30,000. If the highest and lowest price
computers are sold out then the average price of the
remaining 78 computers is Rs. 29,500. The cost of the
highest price computer is Rs. 80,000. The cost of
lowest price computer is:
(a) Rs. 19,000 (b) Rs. 20,000 (c) Rs. 29,
(d) can’t be determined (e) None of these
15. Eleven years earlier the average age of a family of 4
members was 28 years. Now the age of the same
family with six members is yet the same, even when 2
children were born in this period. If they belong to the
same parents and the age of the first child at the time
of the birth of the younger child was same as there
were total family members just after the birth of the
youngest member of this family, then the present age
of the youngest member of the family is :
(a) 3 years (b) 5 years (c) 6 years
(d) 4 years (e) None of these
16. Mr. Patel walked 6 km to reach the station from his
house, then he boarded a train whose average speed
was 60 km/hr and thus he reached his destination. In
this way he took total of 3 hours. If the average speed
of the entire journey was 32 km/hr then the average
speed of walking is :
(a) 3 km/hr (b) 4.5 km/hr (c) 4 km/hr
(d) 5 km/hr (e) None of these
17. The average marks of Sameer decreased by 1, when he
replaced the subject in which he has scored 40 marks
by the other two subjects in which he has just scored
23 and 25 marks respectively. Later he has also
included 57 marks of Computer Science, then the
average marks increased by 2. How many subjects
were there initially?
(a) 6 (b) 12 (c) 15
(d) can’t be determined (e) None of these
18. The average age of Donald, his wife and their two
children is 23 years. His wife is just 4 year younger
than Donald himself and his wife was 24 years old
when his daughter was born. He was 32 years old
when his son was born. Th average age of Donald and
his daughter is :
(a) 25 years (b) 22.5 years (c) 26 years
(d) can’t be determined (e) None of these
19. There are 6 consecutive odd numbers in increasing
order. The difference between the average of the
squares of the first 4 numbers and the last four
numbers is 64. If the sum of the squares of the first and
the last element (i.e., odd numbers) is 178, then the
average of all the six numbers is:
(a) 7 (b) 8 (c) 9
(d) 10 (e) None of these
20. The average age of board of directors of a company,
having 10 directors was 48 years. Coincidentally when
a director aged 53 resigned from the board of
directors, another director died on the same day. So a
new director joined the board of directors aged 34.
Next year in the same month the average age of all the
9 directors was found to be 46 years. The age of the
late (i.e., dead) director at the time of his death was :
(a) 56 years (b) 53 years (c) 57 years
(d) 61 years (e) None of these
1. The ratio of ages of A and B 4 years ago was 5 : 3. The
sum of present ages of A, B and C is 80 years. If present
age of C is equal to sum of present ages of A and B. find
the present age of A.
(a) 17 years (b) 24 years (c) 20 years
(d) 22 years (e) 18 years
IBPS PO Prelims 2019
2. Ratio of age of P 2 years ago to age of R 2 years hence
is 1 : 2 and Q’s present age is 25% more than P’s
present age. If average of present age of P & R is 39
years, then find difference between P’s age 5 years
hence and R’s present age.
(a) 12 years (b) 17 years (c) 21 years
(d) 15 years (e) 14 years
IBPS Clerk Prelims 2019
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18. Average of 10 numbers is 35. If average of first 5
numbers is 40 and average of last 3 numbers is 22,
then what is the average of remaining two numbers?
(a) 36 (b) 32 (c) 40
(d) 42 (e) 44
RBI Assistant Prelims 2020
19. Ratio of present age of A to B is 4 : 3. If C is 4 years
younger to B and difference between present age of A
and B is 4 years, then what is C’s age 10 years hence?
(a) 12 years (b) 22 years (c) 18 years
(d) 20 years (e) 24 years
RBI Assistant Prelims 2020
20. Four years hence, sum of ages of A and B will be 16
years more than the sum of present age of B and C.
Four years ago, sum of age of A and C is 32 years then
find the present age of C?
(a) 24 years (b) 20 years (c) 12 years
(d) 16 years (e) 18 years
SBI PO Prelims 2019
21. 4 years ago, ratio of Shivam’s age to Deepak’s age was
2: 3 and ratio of Shivam’s age 4 years ago to Deepak’s
age 5 years hence is 8: 15. Find present age of Shivam.
(a) 32 years (b) 28 years (c) 40 years
(d) 24 years (e) 36 years
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22. Ratio of present age of A to that of B is 2 : 5, ratio of
present age of B to that of C is 25 : 18 and ratio of
present age of C to that of D is 12 : 13. If D is 11 years
younger than B, then find present age of A.
(a) 24 years (b) 20 years (c) 28 years
(d) 30 years (e) 18 years
SBI Clerk Mains 2019
23. The average of 6 numbers is 20. If one number is
removed, the average becomes 15. What is the number
removed?
(a) 5 (b) 35 (c) 112
(d) 45 (e) None of these
24. After replacing an old member by a new member, it
was found that the average age of five members of a
club is the same as it was 3 yr ago. The difference
between the ages of the replaced and the new member
is
(a) 2 yr (b) 4 yr (c) 8 yr
(d) 15 yr (e) None of these
25. The average of 5 consecutive integers starting with m
is n. What is the average of 6 consecutive integers
starting with (m + 2)?
(a)
2n+ 5
2
(b) (n +2) (c) (n + 3)
(d)
n+ 5
2
(e) None of these
26. The mean of 100 items was 46. Later on, it was
discovered that an item 16 was misread as 61 and
another item 43 was misread as 34. It was also found
that the number of items was 90 and not 100. Then,
what is the correct mean?
(a) 50 (b) 50.7 (c) 52
(d) 52.7 (e) None of these
27. The average pocket-money of 3 friends A, B, C is Rs. 80
in a particular month. If B spends double and C spends
triple of what A spends during that month and if the
average of their unspent pocket-money is Rs. 60, then
A spends (in Rs.)
(a) 10 (b) 20 (c) 30
(d) 40 (e) None of these
28. The batting average of a cricket player for 64 innings
is 62 runs. His highest score exceeds his lowest score
by 180 runs. Excluding these two innings, the average
of remaining innings becomes 60 runs. His highest
score was
(a) 180 runs (b) 209 runs (c) 212 runs
(d) 214 runs (e) None of these
29. The average weight of a group of 20 boys was
calculated to be 89.4 kg and it was later discovered
that one weight was misread as 78 kg instead of 87 kg.
The correct average weight is
(a) 88.95 kg (b) 89.25 kg (c) 89.55 kg
(d) 89.85 kg (e) None of these
30. The average of a collection of 20 measurements was
calculated to be 56 cm. But later, it was found that a
mistake had occurred in one of the measurements
which was recorded as 64 cm, but should have been
61 cm. The correct average must be?
(a) 53 cm (b) 54.5 cm (c) 55.85 cm
(d) 56.15 cm (e) None of these
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Solutions
1. (b): New mean = (
19 × 4 + 24
20
) =
100
20
2. (a): Cost of 10 books= Rs (120 + 150) = Rs 270
Average cost = Rs.
10
270
= Rs. 27
3. (d): Total weight of 20 boys = 89.4 × 20 = 1788 kg
Increase in weight due to misreading
= 87 – 78 = 9 kg
Correct weight of 20 boys = 1788 + 9 = 1797 kg
Correct average weight =
20
1797
= 89.85 kg
Shortcut:
Increase in weight = 9 kg.
New average = + =
20
89.4 89.85 kg
9
4. (a): Sum of the Age of 20 boys = 20 × 11 = 220 years
Sum of the Age of 30 girls = 30 × 12 = 360 years
Total age of 20 boys and 30 girls = 220 + 360
= 580 years.
Average age of the whole class =
580
50
= 11.6 years
5. (d): Total even no = =
−
2 2
63 11 52
Sum of the even number between is 11 to 63
2
26
[2 × 12 + (26 – 1) × 2] = 13 [24 + 50]
= 13 × 74 = 962
Average of even numbers between 11 to 63
962
26
6. (b): Total age of 30 girls = 30 × 13 = 390 years
Total age of 18 girls = 18 × 15 = 270 years
∴ Average age of remaining 12 girls =
−
12
390 270
12
120
= 10 years.
7. (b): The sum of 9 numbers = 9× 50 = 450
Sixth number = sum of 9 numbers – (Sum of first 5
numbers + sum of last 3 numbers)
= 450 – (54 × 5 + 52 × 3) = 450 – (270 + 156)
8. (c): Let average of 9 innings = x, Total run = 9x
According to the question
10
9x 100
= x + 8
9x + 100 = 10x + 80 Þ x = 20
Average after 10 innings = 20 + 8 = 28
Shortcut:
Average at the end of 10
th
innings
= (100 – 9 × 8) = 28 runs.
9. (d): Total price of 10 kg Rice = 12 × 10 Þ 120
Total price of 6 kg Rice = 16 × 6 Þ 96
∴ Average =
16
120 96
16
216
= 13.50 kg
10. (b): Total temp of mon + tues + wed + thus
= 4 × 48°C = 192°C
Temp on mon = 42°C
temp on Tue + Wed + Thus = 192° – 42° = 150°C
Total temp for tue + wed + thus + Fri
= 52° × 4 = 208°C
Tem on Friday = 208° – 150° = 58°C
11. (a): Let the 7th number be x.
According to the question
6 × 8 + x = 7 × 10 ⇒ x = 70 – 48 = 22
12. (c): Total expenditure for first 5 months = 120 × 5
= 600 Rs.
Total expenditure for next 7 months = 130× 7
= 910 Rs.
Total income = Total expenditure of the whole
year + saving
= 600 + 910 + 290 = 1800 Rs
Monthly average income =
12
1800
= 150 Rs.
13. (d): Total monthly salary of 20 workers in an office
= 1900 × 20 = Rs. 38000
Total monthly salary of 20 workers and manager
= 2000 × 21 = Rs. 42000
Manager monthly salary = 42000 – 38000
= Rs. 4000
Manager annual salary = 12 × 4000 = Rs. 48000
14. (c): Total age of men = 15 × 10 = 150
Total age of women = 25 × 12 = 300
Average age of the whole club =
40
150 300
450
40
= 11.25 years.
15. (a): Let the average of rest results = x
According to the question
14 × 2 + x × 10 = 15 × 1 2 Þ 10x = 180 – 28
x = ∴ x = 15.
Hence average of the rest is 15.
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9. (b): New average
24 × 𝑥 +
1
4
× 𝑥 × 6 −
3
4
× 𝑥 × 4
𝑥
24 𝑥+ 1. 5 𝑥
𝑥
10. (b): ATQ,
Total weight = (40 × 10) kg = 400 kg
When weight of heaviest and lightest student not
taken into account then total weight
= (41 × 8) = 328 kg
So, weight of heaviest student + weight of lightest
student = (400 – 328) = 72 kg
⇒ 50 + weight of lightest student = 72
weight of lightest student=22 Kg
11. (a): Three year ago, sum of age of Amit, Bittu and Chitu
together = 27 × 3 = 81 years
Four years hence, sum of ages of Amit, Bittu and
Chitu together = 81 + 7 × 3 = 102 years
Let Four years hence
Amit’s age be 7x ⇒Chitu’s age be 10x and Bittu’s
age be 10x– 6
ATQ,
7x+10x–6+10x = 102
⇒ 27x = 108 ⇒ x = 4
Four years hence, Amit’s age = 7×4 = 28 years
Present age of Amit = 28–4 = 24 years
12. (e): Let age of Veer = 4x years
So, age of Ayush will be = 3x years
Age of Veer (4x) =
40
2
- 24 = 44 years
x = 11
Age of Ayush = 3 × 11 = 33 years.
Required difference = 44 – 33 = 11 years.
13. (c): Let ages of Shivam, Avinash, Pradeep be S, A, P
years respectively.
A + 5 = 2P
𝑆
𝐴
4
5
S + A + P = 37
4x + 5x +
5 𝑥+ 5
2
x = 3
present age of Shivam = 4x = 4 X 3 = 12 years
14. (c): Let four years ago age of Neeraj = 2a
So, age of Veer = a + 6
ATQ –
(2a + 12) + (a + 18) = 84
3a = 54
a = 18 years
Age of Veer = (18 + 10) = 28 years
Age of Neeraj = 2 × 18 + 4 = 40 𝑦𝑒𝑎𝑟𝑠
Required ratio = 28 : 40 = 7 : 10
15. (a): Let S 1
series be x, x+1, x+2, x+3 and x+ 4
ATQ −
3x + 3 = 27
x = 8
Second lowest term of T 1
T
1
series – 22, 20, 18, 16
Required average =
22 + 20 + 18 + 16
4
16. (a): Let present age of R be x years.
So, present age of Q = (x + 18) years
And, present age of S = (x + 18 + 6)
= (x + 24) years
And, present age of P = [(𝑥 + 24 ) ×
200
300
] 𝑦𝑒𝑎𝑟𝑠
2 𝑥
3
ATQ,
2 𝑥
3
+ 16 ) + 𝑥 = 33 × 2
2 𝑥+ 3 𝑥
3
5 𝑥
3
⇒ x = 30 years
Required average =
(𝑥+ 18 )+𝑥+(𝑥+ 24 )
3
3 𝑥+ 42
3
= x + 14
= 44 years
17. (c): B – A = 6 ….(i)
Let A
′
s age is → A
Let B
′
sage is → B
Let C
′
s age is → C
B+ 9
C
9
8
9C – 8B = 72 ….(ii)
C = 2A …(iii)
⇒ 18A − 8B = 72
B − 6
− 8B = 72 [∵ 𝐴 = 𝐵 − 6 …
]
10B = 180
B = 18 year
After 5 years B ‘s age = 23 years
18. (e): Let age of priya and Swati be 3x and 4x
respectively.
Age of Shikha = (4x – 6) years
Atq,
3 𝑥+ 4 𝑥+ 4 𝑥− 6
3
11x = 31 × 3 + 6
99
11
Age of shikha = (4 × 9 - 6 ) = 30 years
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19. (d): Let present age of Q be x
Present Age of P = x+ 3
Present Age of R = x– 3
ATQ—
(x+ 3 +x+x – 3 )− 4 × 3
3
3x – 12 = 99
3x = 111
x=37 years
Age of P after 1 year=37+3+1= 41 years
20. (e): Let age of A and B is 3x and 4x years respectively
ATQ,
C’s age =(80-(4x+6)) years
And, (74-4x) - (3x+6) =
Required difference =4 years
21. (d): Let the present age of A and B be 3x years and 2x
years respectively
Present age of C= ( 2 𝑥 + 4 ) ×
16
9
32 𝑥
9
28
9
ATQ
32 𝑥
9
28
9
Present age of B=32 years
22. (b): Let present age of A, B & C be A years, B years & C
years respectively.
A+B+C
3
A + B + C = 93 …(i)
A = C – 1 …(ii)
B =
19C
14
iii
From (i), (ii) and (iii)—
C – 1 +
19C
14
+ C = 93
47C = (93 × 14 +14)
C =
1316
47
C = 28
Age of B =
19 × 28
14
= 38 years
23. (a): Veer + Shivam = 118 years
Veer + Veer + 24 = 118
Veer = 47 years
Shivam = 71 years
Also,
(Ayush + Anurag) – (Anurag + Veer + Shivam) = 24
Ayush = 142 years
So, Ayush + Shivam = 142 + 71 = 213
Required average age =
213
2
= 106. 5 Years
24. (b): 8
Let age of Rahul’s father = 7x
So, Age of Rahul = 7 𝑥 ×
4
7
Age of Rahul’ son 3 year ago = 4 𝑥 ×
1
4
Present age of Rahul’s son = x + 3
7 𝑥+ 4 𝑥+𝑥+ 3
3
⇒ 12x = 99 - 3 = 96
x = 8
Required difference = (7×8) – (8+3) = 45
25. (e): Let present age of B be x years
5 years ago, Age of B = x – 5
5 years ago, age of A = 3(x – 5)
B’s age 5 year hence = x + 5
So,
C’s age 5 year ago =
(x+ 5 )
3
× 5
5x+ 25
3
ATQ
⇒ 3(x – 5) −
5x+ 25
3
= 9x – 45 – 5x – 25 = 30
4x = 100
x = 25
26. (d): Let present age of suman’s son be x yr
Hence, age of suman=(x+25) yr
According to the question,
𝑥+ 7
(𝑥+ 25 )+ 7
1
2
2x+14= x+
x =32 - 14= 18 yrs
27. (c): let the smallest odd number be ‘a’ so next odd
number be ‘a+2’ and so on
th
number = 𝑎 + ( 8 − 1 ) × 2 = 𝑎 + 14 (using AP,
nth term = a + (n-1)d )
ATQ,
𝑎+𝑎+ 2 +⋯+𝑎+ 14
8
8 𝑎 + 56 = 80 (using sum of AP)
80 − 56
8
Since ‘a’ is smallest number, so smallest 4
numbers will be = 3, 5, 7, 9
Required average =
3 + 5 + 7 + 9
4
28. (c): Let present ages of Karan and Arjun be 4x & 3x
years respectively
Present age of Karan = 4 𝑥 = 20 𝑦𝑒𝑎𝑟𝑠
Present age of Arjun = 3 𝑥 = 15 𝑦𝑒𝑎𝑟𝑠
Present age of Mahesh =
20
2
× 5 = 50 𝑦𝑒𝑎𝑟𝑠
Required ratio =
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By solving (i) & (ii)
a = 45, b = 16, c =51, d = 144
Required difference = 51 – 16 = 35
6. (c): Let present age of Rahul, Gopal and Puneet be ‘r’ ,
‘g’ & ‘p’ respectively
ATQ -
r =
7 𝑔
8
------------- (i)
And,
(𝑝− 4 )
( 𝑟+ 4
)
2
3
3p – 12 = 2 𝑟 + 8
3p − 2 𝑟 = 20 -------- (ii)
And given, p =
3 𝑔
4
-------------- (iii)
From (i), (ii) and (iii) we get –
3 ×
3 𝑔
4
− 2 ×
7 𝑔
8
9g – 7g = 80
g = 40 years
p = 30 years
And r = 7 ×
40
8
= 35 years
Required average =
40 + 30 + 35
3
= 35 years
7. (d): Let number of employees in ‘Adda 247’ initially =
n
ATQ –
( 5 𝑛+ 26 )
(𝑛+ 1 )
n = 20
New number of employees in ‘Adda 247’ = 20 + 1=
8. (d): Let present age of Chintu be 5x years
Then present age of Binny=8x years
And present age of Amit=6x years
ATQ
Required average=40 years
9. (a): Let age of Ravi and Vicky, 4 years ago was 5x years
and 6x years respectively
2 years later, age of Ravi=(5x+6) years
Age of Rocky, 2 years later=(
6 𝑥+ 4
4
× 5 ) + 2 𝑦𝑒𝑎𝑟𝑠
ATQ
(5x+6) + (
6 𝑥+ 4
4
× 5 ) + 2 =
x=
required difference= 4 years
10. (d): Let age of A, B, C & D be a, b, c & d years
respectively
ATQ –
a + b = 2c + 12 ------- (i)
a + d = 2c --------- (ii)
Given,
𝑏 +𝑑
2
b + d = 100 -------- (iii)
And,
𝑎+𝑏+𝑐+𝑑
4
a + b + c + d = 200 ------------ (iv)
From (i) & (ii) −
b – d = 12 ------------ (v)
From (iii) & (v) –
2b = 112
b = 56 years
d = 44 years
From (i) (iii) & (iv) –
a + b + c + d = 200
c = 48 years
a = 200 − (56 + 48 + 44)
a = 52 years
Required difference between age of A and C = 52
− 48 = 4 years.
11. (b): ATQ,
Ram’s age = 29 + 5 = 34 years
⇒ 3x + 2 y = 34 _________(1)
Also, x – y = 3 __________(2)
Solving (1) & (2),
x = 8 , y = 5
required average age =
34 + 29 + 8 + 5
4
= 19 years
and ‘y’ yrs respectively.
Then son’s present age =
Then daughter’s present age=
Atq
Again after 3 yrs
On solving the above equation we get 𝑦 =
Mother’s present age= 42 𝑦𝑟𝑠.
13. (d): Total salary of John & Mark = 2 × 25000 =
Total Salary of John & Shane = 2 × 30000 =
Total Salary of John, Mark, Shane = 3 × 27000 =
So, Salary of John =
So, Salary of Mac = 29000 + 4000 = 𝑅𝑠. 33000
Total salary (all 4 members) = 81000 + 33000 =
Required average =
114000
4
5n + 26 = 6n + 6 12. (e): Let the current age of father and mother be ‘x’ yrs
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14. (d): Let present age of Dharam be ‘x years.’
So, present age of Shivam = 2x years
ATQ,
2 𝑥+ 6
𝑥+ 8
17
11
22x + 66 = 17x + 136
5x = 70
x = 14 years
Now, let present age of Deepak be ‘y years’.
So, y + 6 = 2x + 5 + 4
y = 37 – 6
y = 31 years
15. (a): Present average age of family = 27 + 6 =
Let age of elder member out of remaining two
members = x years
ATQ
𝑥 + 𝑥 − 3 + 3 × 65 + 3 × 20 = 33 × 8
𝑥 = 6 years
16. (d): Let total number of students in class XI be ‘N’
Total marks of class XI = NX
Total marks of class after reduction in marks of 15
students = (NX – 15 × 6 ) = (NX − 90 )
ATQ –
(NX − 90 ) = (X − 1. 875 )N
1.875N = 90
N = 48
Total students in class XII = 48 + 16 = 64
Required average =
5120
64
17. (e): Let present age of Manish = x
⇒ Present age of Amit = 1.5x
Manish’s age five years ago = x – 5
Amit’s age five years ago = 2(x−5) = 2x – 10
But amit’s age five years ago also equals to (1.5x –
⇒ 2x – 10 = 1.5x – 5
⇒ 0.5x = 5
⇒ x = 10
Lalit’s age five years hence = 10 + 5 + 1.5 × 10 + 5
Lalit’s present age = 35 – 5 = 30
18. (d): Let the present age of veer be x yr.
Age of Sneha =
𝑥 − 6
18
yr.
ATQ,
𝑥− 6
18
⇒ x – 6 = 3 × 18
⇒ x = 60 yrs.
Age of veer after 6 years = 66 years
Age of Sneha after 6 years = 3 + 6 = 9 years
Required ratio = 22 : 3
19. (c): Rita’s father’s age = 31 × 2 – 28
= 34 yrs
Rita’s age after two yr =
100
300
× ( 36 )
= 12 yr
∴ Rita’s present age = 10 yr
∴ Raju’s present age = ( 10 − 2 ) ×
75
100
= 8 yr
is 3x, y & 4x respectively
ATQ,
3x + y + 4x = 84
7x + y = 84 …(i)
3x + y = 52 ...(ii)
Solving (i) & (ii)
y = 28
3x = 24
4x = 32
Required difference = 32 – 28 = 4
1. (d); (A – 5) : (B – 5) = 3 : 4 ………….(i)
D + E + 10 = 90 ………….(ii)
C - 4 =
1
2
E ………….(iii)
Current age of C = 27 years
According to equation (iii),
1
2
E
E = 46 years
According to equation (iii),
D + 46 + 10 = 90
D = 34 years
∴ Age of D four years ago was 30 years
2. (b); (A – 5) : (B – 5) = 3 : 4 ………….(i)
D + E + 10 = 90 ………….(ii)
C - 4 =
1
2
E ………….(iii)
Current age of A = 17 years
According to equation (i),
17 − 5
𝐵 – 5
3
4
B = 21 years
According to equation (ii),
D + E = 80 years
∴ Required Average =
𝐴 + 𝐵 + 𝐷 + 𝐸
4
118
4
= 29.5 years
Mains Solutions
20. (e): Let present age of Akshita, Sonakshi and Abhishek
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